     INVESTIGATING BAROTROPIC ZONAL FLOW IN JUPITER'S DEEP ATMOSPHERE 
                     USING JUNO GRAVITATIONAL DATA

          Laura Kulowski, Hao Cao, Rakesh Yadav, Jeremy Bloxham

1. Introduction 
2. Explanation of Data Files 
3. Explanation of Results Files 

See paper (https://doi.org/XXXX) for more details 


==============================================================================
1. Introduction 

The zonal winds within Jupiter's atmosphere give rise to the planet's familiar 
banded appearance. For almost fifty years, researchers have debated whether 
the observed winds represent shallow weather-layer dynamics or deep-seated 
convection. With the recent Juno gravitational measurements, we can now infer
possible deep atmospheric zonal flow profiles. In this project, we test a 
barotropic model of zonal flow against the Juno gravitational data. 
  
This repository contains the data necessary to calculate the gravitational 
signals associated with barotropic zonal flows (section 2) and our model 
results (section 3).


==============================================================================
2. Explanation of Data Files 

The flow-induced gravitational signal is calculated using the thermal wind
equation (TWE). Solving the TWE requires two pieces of information: (1) the 
interior zonal flow profile and (2) the background density profile. We fit 
Jupiter's observed surface zonal winds with Legendre polynomials so that 
    
    omega_surf(theta) = sum_{n} omega_n * P_{n}(cos(theta)),   n = 0,..., N
    u_surf(theta) = omega_surf(theta) * sin(theta) 

where n is the degree of the expansion, theta is the colatitude, and P_{n} 
are the Legendre polynomials. A barotropic zonal flow profile can be produced 
by extending the surface winds into the interior along the z-direction to a 
desired depth. 
  

We provide 3 data files related to the TWE calculation. The details of each 
file are listed below. 

  - coefficients_jupiter_observed_surface_zonal_winds.csv 

    Coefficients (i.e., omega_n) for Jupiter's observed surface zonal winds. 
    The different columns provide the coefficients for different subsets of 
    the observed winds: 

        full                90S-90N planetocentric latitude
        NOEJ and SOEJ       20.9S-14.0S and 13.5N-26.4N
        NOEJ                13.5N-26.4N
        SOEJ                20.9S-14.0S 
        midlats             90S-20.9S and 26.4N-90N

    These flow profiles are derived from the December 2016 zonal wind data 
    reported in Tollefson et al. (2017). 


  - coefficients_smooth_basis_surface_zonal_winds.csv

    Coefficients (i.e., omega_n) for smooth mid/high latitude surface zonal 
    flows. The different columns correspond to different smooth mid/high 
    latitude basis flows.  


  - background_density_profile.csv          

    Density as a function of both radius and pressure depth


==============================================================================
3. Explanation of Results Files 

We provide 8 files that document the model results. The details of each file 
are listed below. 

  - observed_winds.pdf                          

    (a) We separate the observed surface zonal winds into three latitudinal 
    regions based on morphology: the equatorial jet (black), the northern and
    southern off-equatorial jets (NOEJ/SOEJ, orange), and the mid/high 
    latitude jets (blue). Gray (white) bands indicate belts (zones). 
    (b) Barotropic zonal flow profiles are generated by extending the NOEJ, 
    SOEJ, and mid/high latitude jets into the interior along the z-direction
    to radial depths d_{i} (dashed lines). The barotropic zonal flow profile
    shown in panel (b) is not to scale. 


  - jns_vs_depth_by_region.pdf                          

    Odd zonal gravitational harmonics as a function of flow depth for barotropic
    zonal flows within the off-equatorial and mid/high latitude jets. The Juno 
    measured values and their 3-sigma uncertainties (Durante et al. (2020)) 
    are shown in black and gray, respectively. When the NOEJ and SOEJ both 
    extend 1244-1253 km deep (red shaded bars), they produce J5, J7, and J9 
    values that are consistent with the Juno measurements.


  - jns_vs_depth_by_region_3d.pdf                      

    Three-dimensional visualization of the J5, J7, and J9 values produced by 
    the (a) the NOEJ and SOEJ and (b) the NOEJ (gray). Flows involving the 
    NOEJ and SOEJ intersect the 3-sigma uncertainty ellipsoid associated with
    the Juno measurements (orange), while flows involving only the NOEJ do not. 
    The 3-sigma uncertainty associated with each harmonic (i.e., the diagonal
    terms in the error covariance matrix) are marked by blue boxes.


  - gaussian_basis_1234.pdf                             

    Basis functions defined at Jupiter's surface that specify the smooth zonal 
    winds in the mid/high latitudes. These basis functions contain one to four 
    jets in each hemisphere. To generate the interior zonal flow profile, we 
    extend each basis function into the interior barotropically to the same
    truncation depth and then linearly combine the four flow fields. The gray 
    shaded bands indicate the latitudes occupied by the equatorial jet, NOEJ,
    and SOEJ. 
    

  - smooth_solutions.pdf                    

    Surface wind profiles with smooth mid/high latitude zonal flow. The 
    truncation depth of the flow is indicated in the top right of each panel 
    and ranges between 1000-1530 km (5-15 kbar). The gray shaded bands 
    indicate the regions occupied by the equatorial jet, NOEJ, and SOEJ.


  - thin_layer.pdf              

    Radial decay functions applied to a zonal wind profile where the observed
    surface winds extend into the interior along the z-direction without decay.
    In the barotropic case (orange), the zonal flow extends 1000 km deep. In 
    the baroclinic case (blue), the zonal flow is constant until it decays 
    rapidly over a 200 km thick layer (blue shaded region). The odd zonal 
    gravitational harmonics produced by the barotropic and baroclinic zonal 
    flows are listed in the table.


  - compare_bt_bc.pdf       
    
    We compare a barotropic solution of the thermal wind equation where the
    observed surface winds extend into the interior to a radial depth of 
    1000 km to baroclinic solutions where the observed surface winds decay 
    exponentially with different scale heights, H. (a) Components of the
    left-hand side of the TWE as a function of cylindrical depth for a jet 
    located at 32N. (b) The density perturbation as a function of radial depth
    for a jet located at 32N.



  - jns_equ.pdf 

    (a) Equatorial zonal flow profile generated by connecting the northern 
    and southern surface wind values, u_{N} and u_{S}, using a sigmoid
    function. (b) Flow velocity as a function of z for the blue highlighted
    cross-section shown in panel (a). The odd zonal gravitational harmonics
    produced by the flow are tabulated and compared to the Juno-derived 
    values.
